Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
656 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #22608050 | C2 | semidirect |
| 5. C2×#14556550 | C4 | semidirect |
| 6. C22×C4×Dic73 | C4 | semidirect |
| 11. #17988467 | C4 | semidirect |
| 174. C73 | #12853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612422 | 2 |
| #22609849 | 2 |
| #22608050 | 2 |
| C73×#1785 | 2 |
| #12853 | 73 |